Momentum transfer in nonequilibrium steady states

Symmetries and Related Physical Balances for Discontinuous Flow Phenomena within the Framework of Lagrange Formalism

By rigorous analysis, it is proven that from discontinuous Lagrangians, which are invariant with respect to the Galilean group, Rankine–Hugoniot conditions for propagating discontinuities can be derived via a straight forward procedure that can be considered an extension of Noether’s theorem. The use of this general procedure is demonstrated in particular for a Lagrangian for viscous flow, reproducing the well known Rankine–Hugoniot conditions for shock waves.

Effective Langevin equations leading to large deviation function of time-averaged velocity for a nonequilibrium Rayleigh piston

We study fluctuating dynamics of a freely movable piston that separates an infinite cylinder into two regions filled with ideal gas particles at the same pressure but different temperatures. To investigate statistical properties of the time-averaged velocity of the piston in the long-time limit, we perturbatively calculate the large deviation function of the time-averaged velocity. Then, we derive an infinite number of effective Langevin equations yielding the same large deviation function as in the original model. Finally, we provide two possibilities for uniquely determining the form of the effective model.

Universal Trade-Off Relation between Power and Efficiency for Heat Engines

For a general thermodynamic system described as a Markov process, we prove a general lower bound for dissipation in terms of the square of the heat current, thus establishing that nonvanishing current inevitably implies dissipation. This leads to a universal trade-off relation between efficiency and power, with which we rigorously prove that a heat engine with nonvanishing power never attains the Carnot efficiency. Our theory applies to systems arbitrarily far from equilibrium, and does not assume any specific symmetry of the model.

Attractor nonequilibrium stationary states in perturbed long-range interacting systems

Isolated long-range interacting particle systems appear generically to relax to nonequilibrium states ("quasistationary states" or QSSs) which are stationary in the thermodynamic limit. A fundamental open question concerns the "robustness" of these states when the system is not isolated. In this paper we explore, using both analytical and numerical approaches to a paradigmatic one-dimensional model, the effect of a simple class of perturbations. We call them "internal local perturbations" in that the particle energies are perturbed at collisions in a way which depends only on the local properties. Our central finding is that the effect of the perturbations is to drive all the very different QSSs we consider towards a unique QSS. The latter is thus independent of the initial conditions of the system, but determined instead by both the long-range forces and the details of the perturbations applied. Thus in the presence of such a perturbation the long-range system evolves to a unique nonequilibrium stationary state, completely different from its state in absence of the perturbation, and it remains in this state when the perturbation is removed. We argue that this result may be generic for long-range interacting systems subject to perturbations which are dependent on the local properties (e.g., spatial density or velocity distribution) of the system itself.

Macroscopically measurable force induced by temperature discontinuities at solid-gas interfaces

We consider a freely movable solid that separates a long tube into two regions, each of which is filled with a dilute gas. The gases in each region are initially prepared at the same pressure but different temperatures. Under the assumption that the pressure and temperatures of gas particles before colliding with the solid are kept constant over time, we show that temperature gaps appearing on the solid surface generate a force. We provide a quantitative estimation of the force, which turns out to be large enough to be observed by a macroscopic measurement.

Fluctuations in partitioning systems with few degrees of freedom

We study the behavior of a moving wall in contact with a particle gas and subjected to an external force. We compare the fluctuations of the system observed in the microcanonical and canonical ensembles, by varying the number of particles. Static and dynamic correlations signal significant differences between the two ensembles. Furthermore, velocity-velocity correlations of the moving wall present a complex two-time relaxation that cannot be reproduced by a standard Langevin-like description. Quite remarkably, increasing the number of gas particles in an elongated geometry, we find a typical time scale, related to the interaction between the partitioning wall and the particles, which grows macroscopically.

Roles of dry friction in the fluctuating motion of an adiabatic piston

The motion of an adiabatic piston under dry friction is investigated to clarify the roles of dry friction in nonequilibrium steady states. We clarify that dry friction can reverse the direction of the piston motion and causes a discontinuity or a cusplike singularity for velocity distribution functions of the piston. We also show that the heat fluctuation relation is modified under dry friction.

Granular Brownian motors: role of gas anisotropy and inelasticity

We investigate the motion of a two-dimensional wedge-shaped object (a granular Brownian motor), which is restricted to move along the x axis and cannot rotate as gas particles collide with it. We show that its steady-state drift, resulting from inelastic gas-motor collisions, is dramatically affected by anisotropy in the velocity distribution of the gas. We identify the dimensionless parameter providing the dependence of this drift on shape, masses, inelasticity, and anisotropy: The anisotropy leads to dramatically enhanced drift of the motor, which should easily be visible in experimental realizations.

Ratchet effect driven by Coulomb friction: the asymmetric Rayleigh piston

The effect of Coulomb friction is studied in the framework of collisional ratchets. It turns out that the average drift of these devices can be expressed as the combination of a term related to the lack of equipartition between the probe and the surrounding bath, and a term featuring the average frictional force. We illustrate this general result in the asymmetric Rayleigh piston, showing how Coulomb friction can induce a ratchet effect in a Brownian particle in contact with an equilibrium bath. An explicit analytical expression for the average velocity of the piston is obtained in the rare collision limit. Numerical simulations support the analytical findings.